This problem has morphed over time and the current version is even more extreme which is the question posed by Badiou of the Multiple, i.e. pure Heterogeneity prior to the arising of the Ultra One which is the basis for both the One and the Many. In other words the One and Many is really a problem under the auspices of countability, but what is the heterogeneity prior to the arising of both One and Many. Badiou in Being and Event and other places calls that the Multiple. The problem is how does the Ultra One arise within the context of the Multiple to produce both One and Many. And the further question is the relation between that and the non-cardinal, i.e. non-dual or non-monadic non-conceptual and non-experiential states like Buddhist Emptiness and Taoist Void. How do non-cardinals relate to the Multiple. This is an open problem. The classic problem of One and Many is a kind of non-problem because underlying both is countability. Another issue which is related is the problem of the relation between set-like and mass-like approaches to things, i.e. in language countable and non-countable nouns. For instance the Ultra One and the Multiple assume that what ever there is prior to countability is set-like rather than mass like. Heidegger on the other hand in Being and Time distinguishes between present-at-hand which is set-like and ready-to-hand which is mass-like modalities of apprehending things in the world by Dasein (being-in-the-world). Thus one of the flaws of Badiou’s idea of the Ultra One and the Multiple is that it is a present-at-hand distinction, and he does not recognize a corresponding ready-to-hand distinction which probably exists.

My own approach to this issue is to distinguish between Set and Mass and their logics which are Syllogistic and Pervasion logics. Sets are composed of particulars which are not repeated unless we allow Lists. Masses are composed of instances which when mixed give Solutions. An example of a Boundary or a Pervasion logic is Bricken’s use of G. Spencer Brown’s Laws of Form. This logic is expounded by N. Hellerstein in Diamond Logic and Delta Logic. Buddhist and Chinese logic in general are pervasion logics. Thus both Emptiness and Void both are thought in pervasion logic contexts. But when we ask what is the non-cardinal (non-dual and non-monadic) alternative to both set and mass then we could talk about ipsities in an aggregate. And with that idea we become free of the extreme of the Ultra One and the Multiple which is merely Set-like and for which we do not have an alternative which is Mass-like. However because there is Geometry and Topology we know that there must be such an opposite extreme even if it has not been formulated philosophically because our culture is oriented toward sets and away from masses.

But because we can re-pose the problem outside the realm of countability, i.e. in terms of sets and masses and their logics then we can talk about ipsities in an aggregate as being non-cardinal representations of the problem. But the question that is not known is whether there is a logic that goes along with Aggregates other than just the tetra-lemma itself (A, ~A, Both, Neither). Ipsities would in Buddhist terms be suchness. And of course Buddhism sees all phenomena as aggregates. To talk about an ipsity in an aggregates invokes reference: Thisness. And of course Thisness is Existential when an actual eventity is picked out from the aggregate. Ipsities are somewhat like what Kant calls singulars. We would expect them to be prior to the projection of a priori synthesis that gives rise to space, time and objects. Space and Time are for Kant both singulars. But we are talking about what is prior to the arising of the object which first is suchness and later becomes Thisness before it shows its essence through the a priori projection of the categories. We might state that suchness appears in the interspace between the object and the noumena as the source of awareness before explicit intentionality of consciousness. Thisness would be the locus of focused awareness without positing a specific thing as such. From Thisness or reference we get eventually to pointing and grasping and thus ready-to-hand and present-at-hand modes of apprehension by Dasein. Dasein is specifically the part of the Human Being that does the a priori projections. Probably Suchness is prior to the SpaceTime projection and Thisness is after the spacetime projection and prior to the categorical projection. And so we are really pealing back the onion of the transcendental subject of appreception here. Suchness is raw sensation as such prior to its being localized, and Thisness is the localization of that sensation prior to its schematization. Schematization takes us into the projection of space and time as templates of intelligibility prior to recognizing what it is that sorts out this from that. Think of the automatic reaction to a snake-like form in your peripheral vision. You will be jumping away from it even before you know that it is there because this reaction is preprogrammed into our instinctual apparatus and occurs mostly unconsciously. What you react to unconsciously is suchness, but the localization of it that gives a vector to your escape that you find yourself doing even before you know anything is there is Thisness, a primordial reference to what you think is there before you even know what it is that orients you in space and time that you discover though your automatic behavior jumping away from it. All this must be prior to ascertaining it as a set or a mass like phenomena. It is a long way from such primordial reactions to the present-at-hand theoretical question of Ultra-one verses Multiple or later One verses Many. However, from the Buddhist perspective everything we see is suchness in aggregates. But suchness is a term for awareness of phenomena in general prior to its instantiation or particularization. When we discuss ipsities then that is something where we can focus on it even though we have not decide what it is yet. Ipsities are the stuff of references which will eventually be taken up by Dasein by pointing or grasping. With reference to Dasein itself they are called existentiells by Heidegger. But with respect to them being non-dasein I have called them ejects previously. Heidegger does not really give a name to what the corresponding non-dasein thing might be prior to the arising of the difference between subject and object. One question might be how ipsities become either existentiells or ejects. Beyond that we might as how existentiell’s coalesce into existentials such as befindlichkeit, rede, verstehen and falling. On the other hand we can discuss how ejects become ontic and are considered eventually from an ontological perspective.